Resource Allocation for Intelligent Reflecting Surfaces Assisted Federated Learning System with Imperfect CSI

Due to its ability to significantly improve the wireless communication efficiency, the intelligent reflective surface (IRS) has aroused widespread research interest. However, it is a challenge to obtain perfect channel state information (CSI) for IRS-related channels due to the lack of the ability to send, receive, and process signals at IRS. Since most of the existing channel estimation methods are developed to obtain cascaded base station (BS)-IRS-user devices (UDs) channel, this paper studies the problem of computation and communication resource allocation of the IRS-assisted federated learning (FL) system based on the imperfect CSI. Specifically, we take the statistical CSI error model into consideration and formulate the training time minimization problem subject to the rate outage probability constraints. In order to solve this issue, the semi-definite relaxation (SDR) and the constrained concave convex procedure (CCCP) are invoked to transform it into a convex problem. Subsequently, a low-complexity algorithm is proposed to minimize the delay of the FL system. Numerical results show that the proposed algorithm effectively reduces the training time of the FL system base on imperfect CSI.